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I just arrived in some international airport and want to explain to the immigration officer that I'm not going there to have fun; I'm working for my company and going there to make a course/class or another kind of job.
So, could I say "I'm here at work" or do I have to use another preposition instead?
When you're being questioned by Immigration, you'd say "I'm here on business" or "I'm here for business purposes." Then they'll ask you what type of work you do, what company you work for, etc.
I agree with Ouisch, in that situation you say "i'm here on business"
however the phrase you said is wrong, becouse you're not in your company
At work: in my company
To work: with purpose of working
by work I haven't heard it before, but I'm just a student
at work, by work, to work? 
Re: at work, by work, to work? 
Re: at work, by work, to work? 
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